Question

Consider the following relation between input x[n] and output y[n] of a discrete system.
$y\left[n\right]={\sum }_{k=0}^{n^2}cos\left(\frac{\pi }{4}K\right)x\left[K\right]$
The system is

• A. casual
• B. linear
• C. time-variant
• D. stable

Answer 1

Answer: (B), (C)

time-variant

(a,b)

• Linear in x[n]
• Upper limit of summation operator is a function of n $\Rightarrow$ Time variant
• $n^2>n\Rightarrow noncausal$
• For input x(n) = $cos\frac{\pi n}{4}$ , system becomes unstable .